Sách Toán – Học Toán – Đề Thi Toán

Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Sat, 20 May 2023 14:07:50 +0000 vi hourly 1 https://wordpress.org/?v=7.1.2 Bất đẳngThức Tuyển Chọn.pdf https://booktoan.com/bat-dangthuc-tuyen-chon-pdf.html https://booktoan.com/bat-dangthuc-tuyen-chon-pdf.html#respond Mon, 15 May 2023 13:42:58 +0000 https://booktoan.com/bat-dangthuc-tuyen-chon-pdf.html https://booktoan.com/bat-dangthuc-tuyen-chon-pdf.html/feed 0 Cho $x,y,z$ là các số thực thay đổi, đôi một khác nhau thuộc đoạn $\left[ {0;2} \right]$. Tìm giá trị nhỏ nhất của biểu thức $P = \frac{1}{{{{\left( {x – y} \right)}^2}}} + \frac{1}{{{{\left( {y – z} \right)}^2}}} + \frac{1}{{{{\left( {z – x} \right)}^2}}}$. https://booktoan.com/cho-xyz-la-cac-so-thuc-thay-doi-doi-mot-khac-nhau-thuoc-doan-left-02-right-tim-gia-tri-nho-nhat-cua-bieu-thuc-p-frac1left-x-y-right2-frac1.html https://booktoan.com/cho-xyz-la-cac-so-thuc-thay-doi-doi-mot-khac-nhau-thuoc-doan-left-02-right-tim-gia-tri-nho-nhat-cua-bieu-thuc-p-frac1left-x-y-right2-frac1.html#respond Wed, 27 Oct 2021 07:28:15 +0000 https://booktoan.com/?p=188999 https://booktoan.com/cho-xyz-la-cac-so-thuc-thay-doi-doi-mot-khac-nhau-thuoc-doan-left-02-right-tim-gia-tri-nho-nhat-cua-bieu-thuc-p-frac1left-x-y-right2-frac1.html/feed 0 Cho $1 \ne a > 0$, chứng minh rằng: $\frac{{\ln a}}{{a – 1}} \le \frac{{1 + \sqrt[3]{a}}}{{a + \sqrt[3]{a}}}$ https://booktoan.com/cho-1-ne-a-0-chung-minh-rang-fracln-aa-1-le-frac1-sqrt3aa-sqrt3a.html https://booktoan.com/cho-1-ne-a-0-chung-minh-rang-fracln-aa-1-le-frac1-sqrt3aa-sqrt3a.html#respond Sat, 23 Oct 2021 14:31:27 +0000 https://booktoan.com/?p=188975 https://booktoan.com/cho-1-ne-a-0-chung-minh-rang-fracln-aa-1-le-frac1-sqrt3aa-sqrt3a.html/feed 0 Đề bài: Giả sử $x,y$ liên hệ với nhau bởi hệ thức $3x^2+4xy+3y^2=14$. Chứng minh $\frac{14}{5} \leq x,y \leq 14$ https://booktoan.com/de-bai-gia-su-xy-lien-he-voi-nhau-boi-he-thuc-3x24xy3y214-chung-minh-frac145-leq-xy-leq-14.html https://booktoan.com/de-bai-gia-su-xy-lien-he-voi-nhau-boi-he-thuc-3x24xy3y214-chung-minh-frac145-leq-xy-leq-14.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-gia-su-xy-lien-he-voi-nhau-boi-he-thuc-3x24xy3y214-chung-minh-frac145-leq-xy-leq-14.html https://booktoan.com/de-bai-gia-su-xy-lien-he-voi-nhau-boi-he-thuc-3x24xy3y214-chung-minh-frac145-leq-xy-leq-14.html/feed 0 Đề bài: Chứng minh rằng với 3 số dương $a,b,c$ bất kì, ta luôn có: $\frac{{{a^3}}}{{{a^2} + ab + {b^2}}} + \frac{{{b^3}}}{{{b^2} + bc + {c^2}}} + \frac{{{c^3}}}{{{c^2} + ca + {a^2}}} \ge \frac{{a + b + c}}{3}$ https://booktoan.com/de-bai-chung-minh-rang-voi-3-so-duong-abc-bat-ki-ta-luon-co-fraca3a2-ab-b2-fracb3b2-bc-c2-fracc3c2-ca-a2-ge-fraca.html https://booktoan.com/de-bai-chung-minh-rang-voi-3-so-duong-abc-bat-ki-ta-luon-co-fraca3a2-ab-b2-fracb3b2-bc-c2-fracc3c2-ca-a2-ge-fraca.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-voi-3-so-duong-abc-bat-ki-ta-luon-co-fraca3a2-ab-b2-fracb3b2-bc-c2-fracc3c2-ca-a2-ge-fraca.html https://booktoan.com/de-bai-chung-minh-rang-voi-3-so-duong-abc-bat-ki-ta-luon-co-fraca3a2-ab-b2-fracb3b2-bc-c2-fracc3c2-ca-a2-ge-fraca.html/feed 0 Đề bài: Dùng bất đẳng thức Cô-si, tìm GTNN:a)$y=x+\frac{3}{x}; (x>0) $ b) GTNN $y=x+\frac{2}{x-3}; (x>3) $c) $y=5^{x+1}+5^{x-2} $ d) $y=\frac{2 x^{2}+3x+7 }{x} . (x>0)$ https://booktoan.com/de-bai-dung-bat-dang-thuc-co-si-tim-gtnnayxfrac3x-x0.html https://booktoan.com/de-bai-dung-bat-dang-thuc-co-si-tim-gtnnayxfrac3x-x0.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-dung-bat-dang-thuc-co-si-tim-gtnnayxfrac3x-x0.html 0) $ b) GTNN $y=x+\frac{2}{x-3}; (x>3) $c) $y=5^{x+1}+5^{x-2} $ d) $y=\frac{2 x^{2}+3x+7 }{x} . (x>0)$ Lời giải Đề bài: Dùng bất đẳng thức Cô-si, tìm GTNN:a)$y=x+\frac{3}{x}; (x>0) $ […]]]> https://booktoan.com/de-bai-dung-bat-dang-thuc-co-si-tim-gtnnayxfrac3x-x0.html/feed 0 Đề bài: Cho $x,y,z>0; xyz=1$.Tìm giá trị lớn nhất của biểu thức: $P=\frac{1}{x^2+2y^2+3}+\frac{1}{y^2+2z^2+3}+\frac{1}{z^2+2x^2+3}$. https://booktoan.com/de-bai-cho-xyz0-xyz1-tim-gia-tri-lon-nhat-cua-bieu-thuc-pfrac1x22y23frac1y22z23frac1z22x23.html https://booktoan.com/de-bai-cho-xyz0-xyz1-tim-gia-tri-lon-nhat-cua-bieu-thuc-pfrac1x22y23frac1y22z23frac1z22x23.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-xyz0-xyz1-tim-gia-tri-lon-nhat-cua-bieu-thuc-pfrac1x22y23frac1y22z23frac1z22x23.html https://booktoan.com/de-bai-cho-xyz0-xyz1-tim-gia-tri-lon-nhat-cua-bieu-thuc-pfrac1x22y23frac1y22z23frac1z22x23.html/feed 0 Đề bài: Cho $xy=4 (x>0, y>0)$. Tìm giá trị nhỏ nhất của:1) $x^{2}+y^{2}$2) $x^{4}+y^{4}$3) $(x+1)(4y+3)$ https://booktoan.com/de-bai-cho-xy4-x0-y0-tim-gia-tri-nho-nhat-cua1-x2y22-x4y43-x14y3.html https://booktoan.com/de-bai-cho-xy4-x0-y0-tim-gia-tri-nho-nhat-cua1-x2y22-x4y43-x14y3.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-xy4-x0-y0-tim-gia-tri-nho-nhat-cua1-x2y22-x4y43-x14y3.html 0, y>0)\). Tìm giá trị nhỏ nhất của:1) $x^{2}+y^{2}$2) $x^{4}+y^{4}$3) $(x+1)(4y+3)$ Lời giải Đề bài: Cho $xy=4 (x>0, y>0)$. Tìm giá trị nhỏ nhất của:1) $x^{2}+y^{2}$2) $x^{4}+y^{4}$3) $(x+1)(4y+3)$ Lời giải 1) Đặt: $f(x,y)=x^{2}+y^{2}\geq 2xy=8$$\Rightarrow \min f(x,y)=8$ khi $x=y=2$.2) $f(x,y)=x^{4}+y^{4}=(x^{2}+y^{2})^{2}-2x^{2}y^{2}\geq (2xy)^{2}-2x^{2}y^{2}=2x^{2}y^{2}=32$$\Rightarrow \min f(x,y)=\min (x^{4}+y^{4})=32$ khi $x=y=2$3) $f(x,y)=(x+1)(4y+3)=4xy+3x+4y+3$$=19+3x+4y\geq 19+2\sqrt{12.xy}=19+2\sqrt{4.4.3}=19+8\sqrt{3}$$\Rightarrow \min f(x,y)=19+8\sqrt{3}$ khi \(x=\frac{4\sqrt{3}}{3}; […]]]> https://booktoan.com/de-bai-cho-xy4-x0-y0-tim-gia-tri-nho-nhat-cua1-x2y22-x4y43-x14y3.html/feed 0 Đề bài: $a,b,c$ là $3$ số khác $0$. Chứng minh rằng $\frac{{{a^2}}}{{{b^2}}} + \frac{{{b^2}}}{{{c^2}}} + \frac{{{c^2}}}{{{a^2}}} \ge \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ https://booktoan.com/de-bai-abc-la-3-so-khac-0-chung-minh-rang-fraca2b2-fracb2c2-fracc2a2-ge-fracab-fracbc-fracca.html https://booktoan.com/de-bai-abc-la-3-so-khac-0-chung-minh-rang-fraca2b2-fracb2c2-fracc2a2-ge-fracab-fracbc-fracca.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-abc-la-3-so-khac-0-chung-minh-rang-fraca2b2-fracb2c2-fracc2a2-ge-fracab-fracbc-fracca.html https://booktoan.com/de-bai-abc-la-3-so-khac-0-chung-minh-rang-fraca2b2-fracb2c2-fracc2a2-ge-fracab-fracbc-fracca.html/feed 0 Đề bài: Chứng minh rằng : $abc(a+b)(b+c)(c+a)\leq \frac{8}{729}$. Trong đó $a,b,c $ là các số thực không âm thỏa mãn $a+b+c=1$ https://booktoan.com/de-bai-chung-minh-rang-abcabbccaleq-frac8729-trong-do-abc-la-cac-so-thuc-khong-am-thoa-man-abc1.html https://booktoan.com/de-bai-chung-minh-rang-abcabbccaleq-frac8729-trong-do-abc-la-cac-so-thuc-khong-am-thoa-man-abc1.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-abcabbccaleq-frac8729-trong-do-abc-la-cac-so-thuc-khong-am-thoa-man-abc1.html https://booktoan.com/de-bai-chung-minh-rang-abcabbccaleq-frac8729-trong-do-abc-la-cac-so-thuc-khong-am-thoa-man-abc1.html/feed 0